Integrator.



L. OTT.

INTEGRATOR.

APPLICATION FILED 00112, 1911.

Patented Sept. 2, 1913.

W/TA/ESSES TTED h TATlilri PATllilNT @FFTQE.

LUDWIG OTT, OF KEMPTEN, GERMANY, ASSIGNOR TO HERD/[ANN OTT, L'UDWIG OTT, AND ADOLF STEIS, COLPARTNERS CONSTITUTING THE PARTNERSHIP OF A. OTI, OF

KEMPTEN, BA'VAEIA, GERMANY.

INTEGRATOR.

Application filed October 12, 1911.

Kempten, Bavaria, Germany, have invented Specification of Letters Patent.

a new and II'IIPI'OVQd Integrator, of which the following is a specification.

My invention relates to integrators, called planimeters, and. has for its object to provide an integrator for mechanical integration based upon the same principle as the well known A'n'lslers polarplaninictcr and adapted on the one hand to the determination of plane areas, 7'. (1., to the evaluation of integrals of the type e f 061 'yclx using Cartesian coordinates, or of the type dfp ne, that The character of my invention will be better understood by reference to the accompanying drawings, which are hereby made a part of this specification, in which Figure 1 is a plan view of a preferred :liorm (it my invention; Fig. 2 is a sectional elevation along the line 2-2 of Fig. t; Fig. 3 an end elevation taken from the left (Figs. 1 and 2); and Fig. t is a diagram illustrating the theory of my invention.

Referring to the drawings my invention consists, essentially, of a main 'lollower A and two directors or guides via, a director arm 13 and a polar director 3. To use the instrument the follower is eniplo'ycd with either one or the other of these two directors according to the character oil? the integration as aforesaid and as will hereafter be described in detail.

The follower A comprises a bar a a havoften Patented Sept. 2,1913.

Serial No. 654,397.

inn a rectangular slideway g cut into its under side tor nearly its entire length and provided at one end with a stylus perpendicular to the working plane and adapted to tollow the bounding curve of the area to be integrated or the curve to be evaluated. The other end of the :liollower A is provided with a blunt supporting point or knoh c projecting 'trom below, and a conical hole j comprising coupling means is sunk into the upper side oi the follower. Fixed laterally to the bar a, 1/ ax ljacen't to the stylus c is an L-shapcd yoke in which is mounted an integrating: roller (Z. This roller must be accurately adjusted so that its axis 71 i1 is exactly parallel to the axis of the :tollower while its plane oli rotation pcrpcndicuhn' to the working surface and preterably (but not necessarily) passes through the stylus c. The axis II- lz. may be at any convenient (listance from the axis of the follower A. Rotation of the roller (Z is read upon the graduated drum 7.: fixed to one side thereof with the aid of a vcrnicr Z. The follower thus has three points of support upon the working plane, via, the stylus, the integrating roller, and the si'lpporting point 0, and is always in stable equilibrium independently of either the director arm or the polar director.

The director arm l) has at one end a dmvnwardly projecting; spindle in which terminates in a ball adapted to be seated in the conical hole f; the other end of arm li engages rcvolubly with a second vertical spindle n'ovidcd with a weight 0 and a pin point n for holding the spindle in any desired location upon the working surface. When the director arm is coupled to the Follower as just described the free end of the l'ollower (the end opposite the one provided with the stylus and the integrating roller) may obviously be swung in a circle the radius at which may be of any convenicnt length. When this radius is intinily the circle becomes a straight line. Any device For compelling the free end of the follower to travel in a determined circle may be considered as an equivalent of the the slideway g g.

director arm specifically described and shown in the drawing.

The polar director C comprises a vertically arranged pin of diameter to just fit within This pin I fix upon a suitable button provided with needle points for attaching it to the working surface.

In the use of my invention'I proceed as follows: For the ordinary determinations of plane areas, the follower A is coupled with the director arm B, and the instrument used exactly as is the well-known polarplanimeter from which it does not differ in function but only in appearance, that is to say, the stylus 0 is made to follow the bounding curve and the integrating roller is read and its value used in connection with the con stants of the instrument. If, on the other hand, integrals of the form are to be evaluated in connection with a roller read as before.

The theory of my invention may be explained as follows, referring to the diagram Fig. 4t:Let G represent the pole a out and through which the follower may be moved, SS be the curve traced by the stylus, P be the starting position of the stylus, P be the corresponding starting position for the integrating roller, Q be the position of the stylus after a differential of the curve has been traced, Q be the position of the integrating roller when the stylus is at Q, OP be a radiusvector or p. Then the angle P O Qzcle. Then in passing from P to Q, the axis 71, h of the integrating roller will include an angle P O Q, or do andthe line P G will be equal tot-he radiusvector p. r

In the above described movement, the stylus 0 will move over an infinitesimally short right line P Q and the integrating roller over a corresponding right line P Q. This movement of the integrating roller can be resolved into two rectangular components, namely, a rotational movement P R of the roller about the pole 0 upon a radius 9 and a sliding movement R Q of the roller in its own axis. Since there is no rotation of the integrating roller for this sliding movement,

the total rotation ofthe roller will be that corresponding to the line P R, that is to say, to pcZo. If now, the stylus is made to follow a curve of finite length, the integrat ing roller will automatically register the summation of the elements pdcp, that 1s to say, will evaluate the lntegral aforesaid. 7

Having described my invention, 1 claim:

1. In an integrator for the determination of'plane areas, the combination of a follower comprising a bar provided at one end with a stylus, and an integrating roller fixed laterally of but axially parallel with said bar, and at the other end with both a supporting point and coupling means, and means adapted to be engaged with said coupling means for limiting to a circular path the movement of the bar end provided with said coupling means, the bar of the,

follower being further provided with means for engaging slidably a fixed polar director. 2. In an integrator for the determination of plane areas, the combination of a follower comprising a bar provided at one end with a stylus, and an integrating roller fixed laterally of but axially parallel with said bar and at the other end with both a supporting point and coupling means, and means adapted to'be engaged with said coupling means for limiting to a circular path the movement of the bar end provided with said coupling means, the bar of the follower being further provided with a longitudinal groove for engaging a fixed pin. 7 V

3. In an integrator for the determination ofplane areas, the combination of a follower comprising a bar provided at one enclivith a stylus, and an integrating roller fixed laterally of but axially parallel with said bar, and a director arm, the other end of the follower bar having a supporting point and further having detachable pivotal engagement with one end of the director arm, while the other end of the director arm is provided with means for revolublyfixing it in a working surface, the bar of the follower being further provided with a longitudinal groove for engaging a fixed pin. 4-. In an integrator for the determination of plane areas, the combination of a follower comprising a bar provided at one end with a stylus and an integrating roller fixed laterally of but axially parallel with said bar, and a director arm, the other end of the follower bar having a supporting point and further having detachable universal engagement with one end of the director arm, while the other end of the director arm is provided with means for revolubly fixing it in a working surface, the bar of the follower being further provided with means for en 'aging slidably a fixed polar direct-or. In an'integrator for the determination oi. plane areas, a follower comprising a bar having a stylus at one end, a supporting point at the other end, and an integrating roller fixed to said bar laterally thereof but axially parallel therewith, the follower being; adapted to rest upon stylus, supporting point and roller, said follower being provided at the end distant from the stylus with a universal bearing point and having further longitudinally arranged means for l) slidably engaging fixed guiding means.

In testimony whereof .I have hereunto set my hand in the presence of two subseriblng Copies of this patent may be obtained for five cents each, by addressing the Commissioner of Patents. Washington, D. G. 

